Problem: In the complex plane, the line segment with end-points $-11 + 3i$ and $3 - 7i$ is plotted in the complex plane.  Find the complex number corresponding to the mid-point of this line segment.
The midpoint of the line segment is given by the average of the end-points, which is
\[\frac{(-11 + 3i) + (3 - 7i)}{2} = \boxed{-4 - 2i}.\][asy]
unitsize(0.4 cm);

pair A, B, M;

A = (-11,3);
B = (3,-7);
M = (A + B)/2;

draw(A--B);

dot("$-11 + 3i$", A ,NW);
dot("$3 - 7i$", B, SE);
dot("$-4 - 2i$", M, NE);
[/asy]